Heated air induction systems are unsightly and power robbing if not designed/managed well.
Early Rochester v-engine carbs had a base heated by exhaust directed from one bank manifold through a passage in the head, then the inlet manifold, through a passage in the carb base, and through the other head into the opposite manifold---when the heat valve(heat riser)was closed by a thermostatic spring--if the passages weren't plugged by carbon.
I remember some spacers under the carb from the Blue Oval(also choke housings) heated by water taken from the engine like the heater supply.
This could be managed by a cable operated manual valve and a caring operator if you can find or fab a suitable spacer.
Get creative, and let us know how you did it--we might have the same need.